source: lemon-0.x/src/hugo/suurballe.h @ 901:69a8e672acb1

// -*- c++ -*-
#ifndef HUGO_SUURBALLE_H
#define HUGO_SUURBALLE_H

///\ingroup flowalgs
///\file
///\brief An algorithm for finding k paths of minimal total length.


#include <hugo/maps.h>
#include <vector>
#include <hugo/min_cost_flow.h>

namespace hugo {

/// \addtogroup flowalgs
/// @{

  ///\brief Implementation of an algorithm for finding k edge-disjoint paths between 2 nodes 
  /// of minimal total length 
  ///
  /// The class \ref hugo::Suurballe implements
  /// an algorithm for finding k edge-disjoint paths
  /// from a given source node to a given target node in an
  /// edge-weighted directed graph having minimal total weight (length).
  ///
  ///\warning Length values should be nonnegative.
  /// 
  ///\param Graph The directed graph type the algorithm runs on.
  ///\param LengthMap The type of the length map (values should be nonnegative).
  ///
  ///\note It it questionable if it is correct to call this method after
  ///%Suurballe for it is just a special case of Edmond's and Karp's algorithm
  ///for finding minimum cost flows. In fact, this implementation is just
  ///wraps the MinCostFlow algorithms. The paper of both %Suurballe and
  ///Edmonds-Karp published in 1972, therefore it is possibly right to
  ///state that they are
  ///independent results. Most frequently this special case is referred as
  ///%Suurballe method in the literature, especially in communication
  ///network context.
  ///\author Attila Bernath
  template <typename Graph, typename LengthMap>
  class Suurballe{


    typedef typename LengthMap::ValueType Length;
    
    typedef typename Graph::Node Node;
    typedef typename Graph::NodeIt NodeIt;
    typedef typename Graph::Edge Edge;
    typedef typename Graph::OutEdgeIt OutEdgeIt;
    typedef typename Graph::template EdgeMap<int> EdgeIntMap;

    typedef ConstMap<Edge,int> ConstMap;

    //Input
    const Graph& G;

    //Auxiliary variables
    //This is the capacity map for the mincostflow problem
    ConstMap const1map;
    //This MinCostFlow instance will actually solve the problem
    MinCostFlow<Graph, LengthMap, ConstMap> mincost_flow;

    //Container to store found paths
    std::vector< std::vector<Edge> > paths;

  public :


    /// The constructor of the class.
    
    ///\param _G The directed graph the algorithm runs on. 
    ///\param _length The length (weight or cost) of the edges. 
    Suurballe(Graph& _G, LengthMap& _length) : G(_G),
      const1map(1), mincost_flow(_G, _length, const1map){}

    ///Runs the algorithm.

    ///Runs the algorithm.
    ///Returns k if there are at least k edge-disjoint paths from s to t.
    ///Otherwise it returns the number of found edge-disjoint paths from s to t.
    ///
    ///\param s The source node.
    ///\param t The target node.
    ///\param k How many paths are we looking for?
    ///
    int run(Node s, Node t, int k) {

      int i = mincost_flow.run(s,t,k);
    

      //Let's find the paths
      //We put the paths into stl vectors (as an inner representation). 
      //In the meantime we lose the information stored in 'reversed'.
      //We suppose the lengths to be positive now.

      //We don't want to change the flow of mincost_flow, so we make a copy
      //The name here suggests that the flow has only 0/1 values.
      EdgeIntMap reversed(G); 

      for(typename Graph::EdgeIt e(G); e!=INVALID; ++e) 
        reversed[e] = mincost_flow.getFlow()[e];
      
      paths.clear();
      //total_length=0;
      paths.resize(k);
      for (int j=0; j<i; ++j){
        Node n=s;
        OutEdgeIt e;

        while (n!=t){


          G.first(e,n);
          
          while (!reversed[e]){
            ++e;
          }
          n = G.head(e);
          paths[j].push_back(e);
          //total_length += length[e];
          reversed[e] = 1-reversed[e];
        }
        
      }
      return i;
    }

    
    ///Returns the total length of the paths
    
    ///This function gives back the total length of the found paths.
    ///\pre \ref run() must
    ///be called before using this function.
    Length totalLength(){
      return mincost_flow.totalLength();
    }

    ///Returns the found flow.

    ///This function returns a const reference to the EdgeMap \c flow.
    ///\pre \ref run() must
    ///be called before using this function.
    const EdgeIntMap &getFlow() const { return mincost_flow.flow;}

    /// Returns the optimal dual solution
    
    ///This function returns a const reference to the NodeMap
    ///\c potential (the dual solution).
    /// \pre \ref run() must be called before using this function.
    const EdgeIntMap &getPotential() const { return mincost_flow.potential;}

    ///Checks whether the complementary slackness holds.

    ///This function checks, whether the given solution is optimal.
    ///It should return true after calling \ref run() 
    ///Currently this function only checks optimality,
    ///doesn't bother with feasibility
    ///It is meant for testing purposes.
    ///
    bool checkComplementarySlackness(){
      return mincost_flow.checkComplementarySlackness();
    }

    ///Read the found paths.
    
    ///This function gives back the \c j-th path in argument p.
    ///Assumes that \c run() has been run and nothing changed since then.
    /// \warning It is assumed that \c p is constructed to
    ///be a path of graph \c G.
    ///If \c j is not less than the result of previous \c run,
    ///then the result here will be an empty path (\c j can be 0 as well).
    ///
    ///\param Path The type of the path structure to put the result to (must meet hugo path concept).
    ///\param p The path to put the result to 
    ///\param j Which path you want to get from the found paths (in a real application you would get the found paths iteratively)
    template<typename Path>
    void getPath(Path& p, size_t j){

      p.clear();
      if (j>paths.size()-1){
        return;
      }
      typename Path::Builder B(p);
      for(typename std::vector<Edge>::iterator i=paths[j].begin(); 
          i!=paths[j].end(); ++i ){
        B.pushBack(*i);
      }

      B.commit();
    }

  }; //class Suurballe

  ///@}

} //namespace hugo

#endif //HUGO_SUURBALLE_H